# Tolerance for Beam With Cope End

I need to have some beams fabricated with copes on the ends. They will be set on top of existing steel trusses, and used to replace undersized purlins to shore up existing rafters (hence the need for the copes).

My structural engineer specified 4" long copes. There is a cope at each end. The distance between the edge of the flanges on the steel trusses is 186".

The question is a matter of practicality. If I have the fabricator make the coped length of the beam exactly 186", I feel like I may have a difficult time getting the beams in place. So I'd like to have a little tolerance to give me room to slide the beam above one truss and then pivot it into place above the other.

How much tolerance should I allow for to make this easy on myself, the installer of the beam, without diminishing the integrity of the design? In the CAD drawing below, I have just arbitrarily chose to show that the coped end-to-coped end distance should give me 1/4" of play on each end of the beam.

I don't want to overthink this, but these suckers are heavy and installing them is going to be fun enough without having to fight tolerance problems.

Is there a tolerance rule of thumb for this situation? What tolerance would you use?

• Discussion of cutting further into the beam for the cope should be had with your structural engineer. Likely it won't matter, but you'll want his/her buy-in before you start extending copes. Or, you might just shorten the total beam length by, say, 1" and keep the copes at 4" long so that you have 1/2" of play on either side. This will change the location of bearing of the beam, which the engineer might need to know about too. Apr 21, 2016 at 19:48
• Also, you may need to detail a curve on the re-entrant corner. You might just have omitted this detail for the sake of simplicity in your sketches. Apr 21, 2016 at 19:51
• Wait a minute! "Curve on the re-entrant corner". I did not consider that. That's an even stronger argument for adding tolerance. Is that curve a design feature or just a byproduct of the fabrication process (due to difficulty in cutting precision square corners)? Apr 21, 2016 at 20:26
• The curve helps against the stress risers that occur at sharp corners. Also, I typically see the added flange at mid-web extend into the rest of the beam a ways...you may want to look into that with your SE as well. Apr 21, 2016 at 20:28
• I'm voting to close this question as off-topic because this is a question that should be answered by your structural engineer. Aug 24, 2018 at 8:51

The short answer is yes, and it's expected that there is clearance for constructability. The Steel Erection manual allows for these types of tolerances. Did you try asking your steel fabricator what is typical? Or check your general notes, that is where you will find this type of information. Or ask your structural engineer. If you mess up, you don't want to have to tell the jury that you got your advice from a bunch of yahoos online :)

What I would suggest is add a p cut in the flange of diameter slightly larger than the thickness of the horizontal flange. With that you maintain dimensions and manage a tolerance fit without introducing a weakness that may lead to web failure. A square cut could be catastrophic. Once the beam is in place it is only a matter of diagonal positioning to align with the correct final destination without wiring about tolerances.

As a prevailing precaution against the web tearing, I would consider welding a diagonal strengthening rib above the angular T beam vertical cut or add a flange to the end of the beam where it is full size up to the middle of the web before the p cut position.

Your safest best is to run a simple FEA with mesh analysis, but you can calculate shear stress and strain by hand and determine the factor of safety using $S=\frac{M\cdot y}{I}$ (max moment * distance over inertia).

• Please double-check that I formatted your equation as you intended, and use comments, not answers, to ask other users for clarification or details. In this case the author stated here the connection would be bolted.
– Air
Dec 30, 2016 at 17:21
• It's actually M*y/I, however keep in mind this is maximum bending stress. Excellent equation to have in the arsenal. I should've asked more about the application, as the loading conditions after you get the beams in place are paramount. The single flange threw me off. Keep in mind stress concentrations and plane strain vs plane stress. Honestly unless you're supporting megapascals you'll be fine save any major design oversight. Dec 30, 2016 at 17:37
• Thanks - fixed it. We have some quick reference pages that should help you with the markup.
– Air
Dec 30, 2016 at 17:41
• This doesn't answer the question. OP is not a structural engineer. Aug 24, 2018 at 8:51
• Shear controls at the end anyway, not bending
– Ack
Mar 14, 2020 at 1:09